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At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?

According to Plutarch, the Greeks found all the rectangles with
integer sides, whose areas are equal to their perimeters. Can you
find them? What rectangular boxes, with integer sides, have their
surface areas equal to their volumes?

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

The Cantor Set

Age 11 to 14 Challenge Level:

Take a line segment of length 1. We'll call it $C_1$.

Now remove the middle third. Call what's left $C_2$.

Now remove the middle third of each line segment in $C_2$. Call
what's left $C_3$.

We can keep doing this, at each stage removing the middle third of
each of the line segments in $C_n$ to form $C_{n+1}$.

Draw pictures of $C_4$ and
$C_5$.

If we suppose that the end points of $C_1$ are 0 and 1, then we can
mark on the end points of the line segments for the later $C_n$
too. For example, $C_2$ has end points $0$, $\frac{1}{3}$,
$\frac{2}{3}$ and $1$ as shown below.

Draw $C_3$ and label the end
points, and label the end points on your pictures of $C_4$ and
$C_5$.

We can keep removing middle thirds infinitely many times. The set
of points left having done it infinitely many times is called the
Cantor set.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.